OBS (Open Broadcast Software) is a free streaming software option used for streaming stuff on twitch.tv and a slew of other sites out there.
I'm using SoundFlower for a bunch of different things like recording streaming music, and also for streaming audio playing through my desktop to twitch.tv and other live coding stream sites.
Here is how to setup OBS to stream audio playing on my MacBook pro. So if you're on a site like livecoding.tv or similar situation where you are streaming and want to share audio you are playing you can.
1) Install SoundFlower which is now on GitHub as a new guy took it over so that's where you can get the installs now
2) Open Audio MIDI Setup on the Mac OS X
3) Add a new aggregate device and select Built-in microphone and Soundflower (2ch)
4) Add a new Multi-Output Device and select Built-in Output and Soundflower (2ch) and change master device to Soundflower (2ch).
(Note: If you don't select Built-in Output then you're not going to hear a thing through your speakers or headphones.)
5) Open OBS and go to Settings and in the Audio section select Soundflower (2ch) as your Desktop Audio Device and set Mic/Auxiliary Audio Device to your Built-in Microphone or if you're using an external mic, select that.
Open sound and set the output to Multi-Output Device
Now just start a recording to verify it's working before you start to stream live and the mp4 that's created locally should now be playing whatever audio you were streaming.